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In this paper, variational inequality problems (VIPs) defined by generalized monotone and pseudomonotone single-valued and multivalued mappings are considered. Some properties of generalized monotone and pseudomonotone mappings are established. The idea of cutting plane methods, developed originally for solving discrete optimization problems (in particular, integer linear programming problems), is applied for solving the considered VIPs. Mathematics subject classification (2000): 49J40, 65K10, 90C33.

On the solution of variational inequality problems by using cutting plane methods